Find the x- and y-intercept of the line.

–3x + 9y = 18

x-intercept is 9; y-intercept is –3.

x-intercept is –6; y-intercept is 2.

x-intercept is 2; y-intercept is –6.

x-intercept is –3; y-intercept is 9.

1 answer

To find the x-intercept and y-intercept of the line given by the equation \(-3x + 9y = 18\), we can proceed as follows:

  1. Finding the x-intercept: The x-intercept occurs where \(y = 0\). Substituting \(y = 0\) into the equation: \[ -3x + 9(0) = 18 \implies -3x = 18 \implies x = -6 \] Thus, the x-intercept is \((-6, 0)\).

  2. Finding the y-intercept: The y-intercept occurs where \(x = 0\). Substituting \(x = 0\) into the equation: \[ -3(0) + 9y = 18 \implies 9y = 18 \implies y = 2 \] Thus, the y-intercept is \((0, 2)\).

Based on our calculations, the x-intercept is \(-6\) and the y-intercept is \(2\).

The correct option is: x-intercept is –6; y-intercept is 2.